Question: In which part of a accelerating spacecraft does time pass more slowly?
Therefore does time pass more quickly or slowly at high altitudes in a gravitational field.
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Hi James, I've linked an existing question that is the same as yours. Note that for an accelerating rocket the spacetime geometry is Rindler while around the Earth the geometry is Schwarzschild. So although in both cases time runs faster as you move upwards there is a difference between them. – John Rennie Oct 19 '15 at 16:38
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At high altitudes i.e further away from the centre of mass of a large object, the gravity decreases. However, Time passes more slowly when the gravitational potential is high for an observer. Therefore if you moved to a rest position above earth, your time would run faster than that of someone on the ground. Usually we move alot faster when we are at altitudes than on the ground so the velocity negates the lower gravitational effect. So in a spacecraft in orbit for example, time passes slower than on earth.
For some good qualitative explanations you may want to look at videos by Minutephysics or Veritasium
Jaywalker
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1This would be a better answer if you made it quantitative. The weak field expression for time dilation in terms of the gravitational potential is already in lots of answers hereabouts so it's only a copy and past away. – John Rennie Oct 19 '15 at 16:41